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Detectives yesterday revealed they are trying to trace the owner of a dark-coloured car seen with its engine running and passenger door open in a layby behind the house around the time of the attack.

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Police search the surrounding area of the house in Achray Place where Cameron Logan, 23, died and his girlfriend Rebecca Williams, 24, was seriously injured in the New Year's Day fire (Image: Getty Images)

Flowers are left outside the house in Achray Place where Cameron Logan, 23, died and his girlfriend Rebecca Williams, 24, was seriously injured (Image: Getty Images)

Radio journalist Rebecca remains critically ill, and Cameron’s mum Cathy and solicitor dad David were treated after the blaze for the effects of breathing smoke. Police are treating the “horrific and spiteful” attack as murder and attempted murder.

Detective Chief Inspector Paul Livingstone, leading the inquiry, said today police want to trace a dog walker who is seen on CCTV walking past the CCG building site on Craigton Road at 0810.

He describes the dog walker as wearing a hooded jacket and darker trousers, but can’t tell if it is a man or a woman as their hood is up. They were walking a dark-coloured dog with a long tail.

The joggers are described as a man and a woman running together on Craigton Road at the same time. The woman is wearing a bandana, a light top and dark jogging bottoms with dark trainers.

The man has on a hat and a two-tone top with dark bottoms and dark trainers.

He said: “It is crucial that we speak to these people seen on CCTV as they may have seen something important, even unwittingly, that could really help with this investigation.

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“They may have seen the dark-coloured car that reportedly had its engine running in the lay-by on Craigton Road or they may have seen other people out walking, driving, cycling or running, anything that could help us find who is responsible for this fatal fire.

“We have had a report of a further two dog walkers that are understood to have been in the surrounding area around the time of the fire.

Forensic officers at the scene of the fire in Milngavie

“One man was seen in the Craigton Wood area around the time the fire was discovered and is being described as being 5ft11, medium build and wearing a grey hooded top with black trousers. He was walking a brown pit bull dog on a lead.

“Another man was wearing a dark top walking along Craigton Road onto the West Highland Way with two Springer Spaniels.”